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Rather easy problem involving set multiplication

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data
    A = { 1, 1, 2, 5}
    B = [1, 2]

    find A x B

    2. Relevant equations
    not much

    3. The attempt at a solution

    well, the problem itself seems easy enough
    The thing is, I'm not very sure what it means to multiply a set by an interval...

    just need a little help with this detail
     
  2. jcsd
  3. Oct 11, 2011 #2
    But what's confusing is that the set {1,1,2,5} is the same as {1,2,5}, by basic set properties.

    One way of understanding the product of a set by an interval is by considering a subset
    of the product of 2 intervals, say , the interval [1,5], and [1,2] , then {1,2,5}x [1,2] will
    just give you three discrete copies of the interval [1,2]. Or look at the square [0,1]x[0,1] , then {0,1}x[0,1] are just the bottom and the top of the square, respectively.
     
  4. Oct 11, 2011 #3

    SammyS

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    You could express the result using set builder notation.

    For example:

    {1,3}×[0,1] = {(1,y)|0≤y≤1} ∪ {(3,y)|0≤y≤1}

    = {(x,y)|x∊{1,3}, 0≤y≤1}
     
  5. Oct 11, 2011 #4

    The thing is, in the book I'm using, up to this exercise, Unions and the such were not defined yet.

    also I'm not 100% sure that {1,1,2,5} = {1,2,5}
    shouldn't one have cardinality 4 and the other cardinality 3 ?

    might make some difference.
     
  6. Oct 11, 2011 #5

    SammyS

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    List the elements in each set. {1,1,2,5} ; {1,2,5} .
     
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